RT Journal Article
T1 Maximal theorems for weighted analytic tent and mixed norm spaces
A1 Aguilar-Hernández, Tanausú
A1 Mas, Alejandro
A1 Peláez-Márquez, José Ángel
A1 Rättyä, Jouni
K1 Matemáticas aplicadas
AB Let ω be a radial weight, 0 < p, q < ∞ and Γ(ξ) ={z ∈ D : | arg z − arg ξ| < (|ξ| − |z|)} for ξ ∈ D. The averageradial integrability space Lqp(ω) consists of complex-valuedmeasurable functions f on the unit disc D such that∥f ∥qLqp(ω) = 12π2πˆ0⎛⎝1ˆ0|f (reiθ)|pω(r)r dr⎞⎠qpdθ < ∞,and the tent space T qp (ω) is the set of those f for which∥f ∥qT qp (ω) =ˆ∂D⎛⎜⎝ˆΓ(ξ)|f (z)|pω(z) dA(z)1 − |z|⎞⎟⎠qp|dξ| < ∞.Let ℋ(D) denote the space of analytic functions in D. It isshown that the non-tangential maximal operatorf ↦ → N (f )(ξ) = supz∈Γ(ξ)|f (z)|, ξ ∈ D,is bounded from ALqp(ω) = Lqp(ω) ∩ ℋ(D) and AT qp (ω) =T qp (ω) ∩ ℋ(D) to Lqp(ω) and T qp (ω), respectively. These piv-otal inequalities are used to establish further results such asthe density of polynomials in ALqp(ω) and AT qp (ω), and theidentity ALqp(ω) = AT qp (ω) for weights admitting a one-sidedintegral doubling condition. Further, it is shown that any ofthe Littlewood-Paley formulas∥f ∥ALqp(ω) ≍ ∥f (k)(1 − | · |)k∥Lqp(ω) +k−1∑︂j=0|f (j)(0)|,f ∈ ℋ(D),∥f ∥AT qp (ω) ≍ ∥f (k)(1 − | · |)k∥T qp (ω) +k−1∑︂j=0|f (j)(0)|,f ∈ ℋ(D),holds if and only if ω admits a two-sided integral doublingcondition. It is also shown that the boundedness of the clas-sical Bergman projection Pγ , induced by the standard weight(γ + 1)(1 − |z|2)γ , on Lqp(ω) and T qp (ω) with 1 < q, p < ∞ isindependent of q, and is described by a Bekollé-Bonami typecondition.
PB Elsevier
YR 2026
FD 2026
LK https://hdl.handle.net/10630/46445
UL https://hdl.handle.net/10630/46445
LA eng
NO Tanausú Aguilar-Hernández, Alejandro Mas, José Ángel Peláez, Jouni Rättyä, Maximal theorems for weighted analytic tent and mixed norm spaces, Journal of Functional Analysis, Volume 291, Issue 3, 2026, 111513, ISSN 0022-1236
NO Funding for open access charge: Universidad de Málaga / CBUA
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 4 may 2026